On the continued fraction expansion of some hyperquadratic functions

Authors : Khalil AYADI, Fatma TAKTAK

Pages : 191-202

Doi:10.3906/mat-1303-61

View : 13 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we consider continued fraction expansions for algebraic power series over a finite field. Especially, we are interested in studying the continued fraction expansion of a particular subset of algebraic power series over a finite field, called hyperquadratic. This subset contains irrational elements a satisfying an equation a = finsert ignore into journalissuearticles values(ar);, where r is a power of the characteristic of the base field and f is a linear fractional transformation with polynomials coefficients. The continued fraction expansion for these elements can sometimes be given fully explicitly. We will show this expansion for hyperquadratic power series satisfying certain types of equations.
Keywords : Finite fields, formal power series, continued fraction